On approximating operators preserving certain polynomials


The paper centers around a general class of discrete linear positive operators depending on a real parameter \(\alpha \geq 0\) and preserving both the constants and the polynomial \(x^{2}+\alpha x\). Under some given conditions, this sequence of operators forms an approximation process for certain real valued functions defined on an interval \(J\). Two cases are investigated: \(J=[0,1]\) and \(J=\)\([0,\infty )\), respectively. Quantitative estimates are proved in different normed spaces and some particular cases are presented.


Octavian Agratini
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Saddika Tarabie
Faculty of Sciences, Tishrin University, 1267 Latakia, Syria


positive linear operators, Popoviciu-Bohman-Korovkin criterion, Bernstein polynomials, Szasz-Mirakjan operators, Baskakov operators, polynomial weight spaces

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O. Agratini, S. Tarabie, On approximating operators preserving certain polynomials, Automation, Computers, Applied Mathematics, 17 (2008) no. 2, pp. 191-199


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